Apple mobility trends data visualization

Introduction

I this notebook we ingest and visualize the mobility trends data provided by Apple, [APPL1].

We take the following steps:

1. Download the data

2. Import the data and summarise it

3. Transform the data into long form

4. Partition the data into subsets that correspond to combinations of geographical regions and transportation types

5. Make contingency matrices and corresponding heat-map plots

6. Make nearest neighbors graphs over the contingency matrices and plot communities

7. Plot the corresponding time series

Data description

From Apple’s page https://www.apple.com/covid19/mobility

About This Data The CSV file and charts on this site show a relative volume of directions requests per country/region or city compared to a baseline volume on January 13th, 2020. We define our day as midnight-to-midnight, Pacific time. Cities represent usage in greater metropolitan areas and are stably defined during this period. In many countries/regions and cities, relative volume has increased since January 13th, consistent with normal, seasonal usage of Apple Maps. Day of week effects are important to normalize as you use this data. Data that is sent from users’ devices to the Maps service is associated with random, rotating identifiers so Apple doesn’t have a profile of your movements and searches. Apple Maps has no demographic information about our users, so we can’t make any statements about the representativeness of our usage against the overall population.

Observations

The observations listed in this subsection are also placed under the relevant statistics in the following sections and indicated with “Observation”.

• The directions requests volumes reference date for normalization is 2020-01-13 : all the values in that column are \(100\).

• From the community clusters of the nearest neighbor graphs (derived from the time series of the normalized driving directions requests volume) we see that countries and cities are clustered in expected ways. For example, in the community graph plot corresponding to “{city, driving}” the cities Oslo, Copenhagen, Helsinki, Stockholm, and Zurich are placed in the same cluster. In the graphs corresponding to “{city, transit}” and “{city, walking}” the Japanese cities Tokyo, Osaka, Nagoya, and Fukuoka are clustered together.

• In the time series plots the Sundays are indicated with orange dashed lines. We can see that from Monday to Thursday people are more familiar with their trips than say on Fridays and Saturdays. We can also see that on Sundays people (on average) are more familiar with their trips or simply travel less.

Load packages

library(Matrix)
library(tidyverse)

Registered S3 methods overwritten by 'dbplyr':
  method         from
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  print.tbl_sql      
── Attaching packages ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse 1.3.1 ──
✓ ggplot2 3.3.5     ✓ purrr   0.3.4
✓ tibble  3.1.4     ✓ dplyr   1.0.7
✓ tidyr   1.1.3     ✓ stringr 1.4.0
✓ readr   2.0.1     ✓ forcats 0.5.1
── Conflicts ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
x tidyr::expand() masks Matrix::expand()
x dplyr::filter() masks stats::filter()
x dplyr::lag()    masks stats::lag()
x tidyr::pack()   masks Matrix::pack()
x tidyr::unpack() masks Matrix::unpack()

library(ggplot2)
library(gridExtra)

Attaching package: ‘gridExtra’

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library(d3heatmap)

======================
Welcome to d3heatmap version 0.9.0

Type citation('d3heatmap') for how to cite the package.
Type ?d3heatmap for the main documentation.

The github page is: https://github.com/talgalili/d3heatmap/
Please submit your suggestions and bug-reports at: https://github.com/talgalili/d3heatmap/issues
You may ask questions at stackoverflow, use the r and d3heatmap tags: 
     https://stackoverflow.com/questions/tagged/d3heatmap
======================


Attaching package: ‘d3heatmap’

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    print

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library(igraph)

Attaching package: ‘igraph’

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    as_data_frame, groups, union

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library(zoo)

Attaching package: ‘zoo’

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    as.Date, as.Date.numeric

library(forecast)

Data ingestion

Apple mobile data was provided in this WWW page: https://www.apple.com/covid19/mobility , [APPL1]. (The data has to be download from that web page – there is an “agreement to terms”, etc.)

dfAppleMobility <- read.csv( "~/Downloads/applemobilitytrends-2021-09-19.csv", stringsAsFactors = FALSE)
#dfAppleMobility <- read.csv( "~/Downloads/applemobilitytrends-2021-02-20.csv", stringsAsFactors = FALSE)
#dfAppleMobility <- read.csv("https://covid19-static.cdn-apple.com/covid19-mobility-data/2024HotfixDev18/v3/en-us/applemobilitytrends-2021-01-15.csv")
names(dfAppleMobility) <- gsub( "^X", "", names(dfAppleMobility))
names(dfAppleMobility) <- gsub( ".", "-", names(dfAppleMobility), fixed = TRUE)

dfAppleMobility

Observation: The directions requests volumes reference date for normalization is 2020-01-13 : all the values in that column are \(100\).

Data dimensions:

dim(dfAppleMobility)

[1] 4691  622

Data summary:

summary(as.data.frame(unclass(dfAppleMobility[,1:3]), stringsAsFactors = TRUE))

           geo_type                  region     transportation_type
 city          : 790   Washington County:  27   driving:3048       
 country/region: 153   Jefferson County :  25   transit: 551       
 county        :2638   Montgomery County:  24   walking:1092       
 sub-region    :1110   Franklin County  :  22                      
                       Madison County   :  21                      
                       Jackson County   :  19                      
                       (Other)          :4553                      

Number of unique “country/region” values:

dfAppleMobility %>% 
  dplyr::filter( geo_type == "country/region") %>% 
  dplyr::pull("region") %>%
  unique %>% 
  length

[1] 63

Number of unique “city” values:

dfAppleMobility %>% 
  dplyr::filter( geo_type == "city") %>% 
  dplyr::pull("region") %>%
  unique %>% 
  length

[1] 295

All unique geo types:

lsGeoTypes <- unique(dfAppleMobility[["geo_type"]])
lsGeoTypes

[1] "country/region" "city"           "sub-region"     "county"        

All unique transportation types:

lsTransportationTypes <-  unique(dfAppleMobility[["transportation_type"]])
lsTransportationTypes

[1] "driving" "walking" "transit"

Data transformation

It is better to have the data in long form (narrow form). For that I am using the package “tidyr”.

# lsIDColumnNames <- c("geo_type", "region", "transportation_type") # For the initial dataset released by Apple.
lsIDColumnNames <- c("geo_type", "region", "transportation_type", "alternative_name", "sub-region", "country" )
dfAppleMobilityLongForm <- tidyr::pivot_longer( data = dfAppleMobility, cols = setdiff( names(dfAppleMobility), lsIDColumnNames), names_to = "Date", values_to = "Value" )
dim(dfAppleMobilityLongForm)

[1] 2889656       8

Remove the rows with “empty” values:

dfAppleMobilityLongForm <- dfAppleMobilityLongForm[ complete.cases(dfAppleMobilityLongForm), ]
dim(dfAppleMobilityLongForm)

[1] 2853808       8

Add the “DateObject” column:

dfAppleMobilityLongForm$DateObject <- as.POSIXct( dfAppleMobilityLongForm$Date, format = "%Y-%m-%d", origin = "1970-01-01" )

Add “day name” (“day of the week”) field:

dfAppleMobilityLongForm$DayName <- weekdays(dfAppleMobilityLongForm$DateObject)

Here is sample of the transformed data:

set.seed(3232)
dfAppleMobilityLongForm %>% dplyr::sample_n( 10 )

Here is summary:

summary(as.data.frame(unclass(dfAppleMobilityLongForm), stringsAsFactors = TRUE))

           geo_type                     region        transportation_type                alternative_name        sub.region               country                Date        
 city          : 484278   Washington County:  16561   driving:1844517                            :2229152             : 812035   United States:1902810   2020-01-13:   4652  
 country/region:  93789   Jefferson County :  15337   transit: 338421     AB                     :   1843   Texas     : 147809   Japan        : 135661   2020-01-14:   4652  
 county        :1618190   Montgomery County:  14730   walking: 670870     ACT                    :   1843   California: 101866                :  93789   2020-01-15:   4652  
 sub-region    : 657551   Franklin County  :  13490                       Andalucía              :   1843   Georgia   :  80345   France       :  55238   2020-01-16:   4652  
                          Madison County   :  12879                       Bayern                 :   1843   Virginia  :  75441   Germany      :  52764   2020-01-17:   4652  
                          Jackson County   :  11653                       BC|Colombie-Britannique:   1843   Florida   :  74259   Thailand     :  41696   2020-01-18:   4652  
                          (Other)          :2769158                       (Other)                : 615441   (Other)   :1562053   (Other)      : 571850   (Other)   :2825896  
     Value           DateObject                       DayName      
 Min.   :   0.44   Min.   :2020-01-13 00:00:00   Friday   :404724  
 1st Qu.:  91.77   1st Qu.:2020-06-15 00:00:00   Monday   :405790  
 Median : 123.72   Median :2020-11-16 00:00:00   Saturday :409376  
 Mean   : 133.41   Mean   :2020-11-15 18:05:16   Sunday   :409376  
 3rd Qu.: 162.47   3rd Qu.:2021-04-19 00:00:00   Thursday :409376  
 Max.   :3303.05   Max.   :2021-09-19 00:00:00   Tuesday  :405790  
                                                 Wednesday:409376  

Partition the data into geo types × transportation types:

dfAppleMobilityLongForm %>% 
  dplyr::group_by( geo_type, transportation_type) %>% 
  dplyr::count()

aQueries <- split(dfAppleMobilityLongForm,  dfAppleMobilityLongForm[,c("geo_type", "transportation_type")] )

Heat-map plots

We can visualize the data using heat-map plots.

Remark: Using the contingency matrices prepared for the heat-map plots we can do further analysis, like, finding correlations or nearest neighbors. (See below.)

Cross-tabulate dates with regions:

aMatDateRegion <- purrr::map( aQueries, function(dfX) { xtabs( formula = Value ~ Date + region, data = dfX, sparse = TRUE ) } )
aMatDateRegion <- aMatDateRegion[ purrr::map_lgl(aMatDateRegion, function(x) nrow(x) > 0 ) ]

dfPlotQuery <- purrr::map_df( aMatDateRegion, Matrix::summary, .id = "Type" )
head(dfPlotQuery)

613 x 295 sparse Matrix of class "dgCMatrix", with 180835 entries 
          Type i j      x
1 city.driving 1 1 100.00
2 city.driving 2 1 100.73
3 city.driving 3 1 102.86
4 city.driving 4 1 102.65
5 city.driving 5 1 109.39
6 city.driving 6 1 109.62

ggplot2::ggplot(dfPlotQuery) +
  ggplot2::geom_tile( ggplot2::aes( x = j, y = i, fill = log10(x)), color = "white") +
  ggplot2::scale_fill_gradient(low = "white", high = "blue") +
  ggplot2::xlab("Region") + ggplot2::ylab("Date") + 
  ggplot2::facet_wrap( ~Type, scales = "free", ncol = 2)

Here we take a “closer look” to one of the plots using a dedicated d3heatmap plot:

d3heatmap::d3heatmap( x = aMatDateRegion[["country/region.driving"]], Rowv = FALSE )

Warning in RColorBrewer::brewer.pal(n, pal) :
  n too large, allowed maximum for palette RdYlBu is 11
Returning the palette you asked for with that many colors

Warning in RColorBrewer::brewer.pal(n, pal) :
  n too large, allowed maximum for palette RdYlBu is 11
Returning the palette you asked for with that many colors

Nearest neighbors graphs

Graphs overview

Here we create nearest neighbor graphs of the contingency matrices computed above and plot cluster the nodes:

th <- 0.94
aNNGraphs <- 
  purrr::map( aMatDateRegion, function(m) { 
    m2 <- cor(as.matrix(m))
    for( i in 1:nrow(m2) ) {
      m2[i,i] <- 0
    }
    m2 <- as( m2, "dgCMatrix") 
    m2@x[ m2@x <= th ] <- 0
    #m2@x[ m2@x > th ] <- 1
    igraph::graph_from_adjacency_matrix(Matrix::drop0(m2), weighted = TRUE, mode = "undirected")
  })

ind <- 3
ceb <- cluster_edge_betweenness(aNNGraphs[[ind]])  
dendPlot(ceb, mode="hclust", main = names(aNNGraphs)[[ind]])

plot(ceb, aNNGraphs[[ind]], vertex.size=1, vertex.label=NA, main = names(aNNGraphs)[[ind]])

Time series analysis

Time series

In this section for each date we sum all cases over the region-transportation pairs, make a time series, and plot them.

Remark: In the plots the Sundays are indicated with orange dashed lines.

Here we make the time series:

aDateStringToDateObject <- unique( dfAppleMobilityLongForm[, c("Date", "DateObject")] )
aDateStringToDateObject <- setNames( aDateStringToDateObject$DateObject, aDateStringToDateObject$Date )
aDateStringToDateObject <- as.POSIXct(aDateStringToDateObject)
aTSDirReqByCountry <-  purrr::map( aMatDateRegion, function(m) rowSums(m) )

matTS <- do.call( cbind, aTSDirReqByCountry)

Warning in (function (..., deparse.level = 1)  :
  number of rows of result is not a multiple of vector length (arg 1)

zooObj <- zoo::zoo( x = matTS, as.POSIXct(rownames(matTS)) )

Here we plot them:

autoplot(zooObj) +
  aes(colour = NULL, linetype = NULL) +
    facet_grid(Series ~ ., scales = "free_y") +
  geom_vline( xintercept = aDateStringToDateObject[weekdays(aDateStringToDateObject) == "Sunday"], color = "orange", linetype = "dashed", size = 0.3 )

Observation: In the time series plots the Sundays are indicated with orange dashed lines. We can see that from Monday to Thursday people are more familiar with their trips than say on Fridays and Saturdays. We can also see that on Sundays people (on average) are more familiar with their trips or simply travel less.

“Forecast”

He we do “forecast” for code-workflow demonstration purposes – the forecasts should not be taken seriously.

Fit a time series model to the time series:

aTSModels <- purrr::map( names(zooObj), function(x) { forecast::auto.arima( zoo( x = zooObj[,x], order.by = index(zooObj) ) ) } )

aTSModels <- purrr::map( names(zooObj), function(x) forecast::forecast( as.matrix(zooObj)[,x] ) )
names(aTSModels) <- names(zooObj)

Plot data and forecast:

lsPlots <- purrr::map( names(aTSModels), function(x) autoplot(aTSModels[[x]]) + ylab("Volume") + ggtitle(x) )
names(lsPlots) <- names(aTSModels)

do.call( gridExtra::grid.arrange, lsPlots )

References

[APPL1] Apple Inc., Mobility Trends Reports, (2020), apple.com.

[AA1] Anton Antonov, “Apple mobility trends data visualization”, (2020), SystemModeling at GitHub.

[AA2] Anton Antonov, “NY Times COVID-19 data visualization”, (2020), SystemModeling at GitHub.